# 5.1: Jars and Jars

**At Grade**Created by: CK-12

Look at the pictures of the pan balances below. What do you see? Can you figure out the weight of jar z? Can you say anything about the weight of jar x? In this concept, we will learn how to use problem solving steps to help us to describe the relative weights of objects given in pan balances.

### Guidance

In order to determine the relationship between the balance pans like the one above, use the problem solving steps to help you.

- First,
**describe**what you see and what information you are given. - Next, identify what
**your job**is and what you are trying to solve. In all of these problems, your job will be to figure out the relative weights of the two jars that have letters of them. - Third, make a
**plan**for how you will solve. See if you can figure out the exact weight of one jar first. Then, describe what you know about the weight of the other jar. - Fourth,
**solve**the problem. - Last,
**check**your answer.

#### Example A

What is the weight of jar p? What could be the weight of jar m? Tell how you figured it out.

**Solution:**

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe} && \text{I see two pan balances. I see two jars} \ m \ \text{and} \ p.\\ &&& \text{Pan Balance} \ D: \ \text{The pans are not balanced}.\\ &&& \text{Pan Balance} \ C: \ \text{The pans are balanced. One pan has a} \ 5 \ \text{pound jar}.\\ & \mathbf{My \ Job} && \text{Figure out a weight for} \ p. \ \text{Then figure out possible weights for m.}\\ & \mathbf{Plan} && \text{Pan Balance} \ D: \ \text{The pan with} \ m \ \text{is lower so,} \ m \ \text{is heavier than} \ p.\\ &&& \text{Pan Balance} \ C: \text{Use the fact that} \ p \ \text{weighs} \ 5 \ \text{pounds}.\\ & \mathbf{Solve} && \text{Pan Balance} \ C: \ p=5 \ \text{pounds.}\\ &&& \text{Pan Balance} \ D: \ m \ \text{has to weigh more than} \ 5 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ C: \ p=5 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ A: \ m \ \text{is more than 5 pounds.} \end{align*}

#### Example B

What is the weight of jar k? What could be the weight of jar j? Tell how you figured it out.

**Solution:** We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe} && \text{I see two pan balances. I see two jars} \ k \ \text{and} \ j.\\ &&& \text{Pan Balance} \ G: \ \text{The pans are not balanced}.\\ &&& \text{Pan Balance} \ H: \ \text{The pans are balanced. One pan has a} \ 6 \ \text{pound jar}.\\ & \mathbf{My \ Job} && \text{Figure out a weight for} \ k. \ \text{Then figure out possible weights for } \ j.\\ & \mathbf{Plan} && \text{Pan Balance} \ G: \ \text{The pan with} \ j \ \text{is lower, so} \ j \ \text{is heavier than} \ k.\\ &&& \text{Pan Balance} \ H: \text{Use the fact that} \ k+k \ \text{weighs} \ 6 \ \text{pounds}.\\ & \mathbf{Solve} && \text{Pan Balance} \ H: \ k+k=6 \ \text{pounds, so} \ k = 3 \ \text{pounds}.\\ &&& \text{Pan Balance} \ G: \ j \ \text{has to weigh more than} \ 3 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ H: \ 3+3=6 \ \text{pounds}.\\ &&& \qquad \qquad \qquad \qquad \ k=3 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ G: \ j \ \text{is more than 3 pounds.} \end{align*}

#### Example C

What is the weight of jar y? What could be the weight of jar z? Tell how you figured it out.

**Solution:**

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe} && \text{I see two pan balances. I see two jars} \ y \ \text{and} \ z.\\ &&& \text{Pan Balance} \ K: \ \text{The pans are not balanced}.\\ &&& \text{Pan Balance} \ J: \ \text{The pans are balanced. One pan has 2} \ 2 \ \text{pound jars}.\\ & \mathbf{My \ Job} && \text{Figure out a weight for} \ y. \ \text{Then figure out possible weights for z.}\\ & \mathbf{Plan} && \text{Pan Balance} \ K: \ \text{The pan with} \ y \ \text{is lower so,} \ y \ \text{is heavier than} \ z.\\ &&& \text{Pan Balance} \ J: \text{Use the fact that} \ y \ \text{weigh} \ 2 + 2 =4 \ \text{pounds}.\\ & \mathbf{Solve} && \text{Pan Balance} \ J: \ y = 4 \ \text{pounds.}\\ &&& \text{Pan Balance} \ K: \ z \ \text{has to weigh less than} \ 4 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ J: \ y=2+2=4 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ K: \ z \ \text{is less than 4 pounds.} \end{align*}

#### Concept Problem Revisited

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe} && \text{I see two pan balances. I see two jars} \ x \ \text{and} \ z.\\ &&& \text{Pan Balance} \ A: \ \text{The pans are not balanced}.\\ &&& \text{Pan Balance} \ B: \ \text{The pans are balanced. One pan has a} \ 12 \ \text{pound jar}.\\ & \mathbf{My \ Job} && \text{Figure out a weight for} \ z. \ \text{Then figure out possible weights for x.}\\ & \mathbf{Plan} && \text{Pan Balance} \ A: \ \text{The pan with} \ z \ \text{is lower so,} \ z \ \text{is heavier than} \ x.\\ &&& \text{Pan Balance} \ B: \text{Use the fact that} \ z+z+z \ \text{weighs} \ 12 \ \text{pounds}.\\ & \mathbf{Solve} && \text{Pan Balance} \ B: \ z + z + z = 12 \ \text{pounds, so} \ z = 4 \ \text{pounds}.\\ &&& \text{Pan Balance} \ A: \ x \ \text{has to weigh less than} \ 4 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ B: \ 4 + 4 + 4 = 12 \ \text{pounds}.\\ &&& \qquad \qquad \qquad \qquad \ z=4 \ \text{pounds}.\\ & \mathbf{Check} && \text{Pan Balance} \ A: \ x \ \text{is less than 4 pounds.} \end{align*}

### Vocabulary

To be ** equal** means to be the same. When pans are

**then the weights of the two pans are**

*balanced***. To be**

*equal***means to be bigger. To be**

*greater than***means to be smaller. When two pans are not**

*less than***then the weight of one pan is**

*balanced***the weight of the other pan.**

*greater than*### Guided Practice

What could be the weight of the jars? Tell how you figured it out.

1.

2.

3.

**Answers:**

1. x is 6 pounds; v is more than 3 pounds

2. w is 4 pounds; t is less than 8 pounds

3. a is 7 pounds; b is less than 7 pounds

### Explore More

What could be the weight of the jars? Tell how you figured it out.

### Image Attributions

Students willfigure out the relative weights of objects from the relationships displayed in pan balances. Students will use problem solving steps to help them.

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